He once said Google should hire a million engineers. Since taking over as CEO in April, he's launched a head-on assault against Facebook with Google+ and shocked the mobile industry by offering a $12.5 billion takeover of Motorola.

The Motorola deal in particular shows how Page thinks. It was four times larger than the company's previous largest buy. It's way outside Google's traditional core businesses -- search and advertising -- and puts Google into potential competition with some of its most important partners.

But it also puts Google right into the heart of one of the most important technology trends of the decade: the move to the mobile Web.

Subtracting the cost of the Motorola deal, Google still has more than than $25 billion in cash and marketable securities on hand. It generated $2.6 billion in free cash flow just last QUARTER.

That kind of cash could buy a lot of interesting companies.

Hulu would make Google an unstoppable force in online video.

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Google has been considering a Hulu bid since July, and was considered a favorite contender as of last week. But over the weekend, the Financial Times reported that only three companies were still left -- Amazon, Yahoo, and the Dish network -- so perhaps Google found the $1.5 to $2 billion price too steep.

Update: AllThingsD's Peter Kafka is now reporting that Google is making a much BIGGER bid for Hulu, but on its own terms -- maybe it's aiming to get more content or a longer exclusive period.

OpenTable could help Google's local commerce plans.

Danny Chen/@KungFoodPanda

LQ@SK's teriyaki rabbit meatballs with foie gras.

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OpenTable could have all sorts of ties to Google's local initiatives -- one of Larry Page's top priorities. Imagine being able to search not just for a restaurant near you, but for a restaurant near you with an open reservation at a particular time, and then book it, all without leaving Google search.

It could also tie to Offers (Google's daily deals service) and Wallet (the NFC-based payments service).

Plus, OpenTable has lost about half its value since April, making it look cheap -- its market cap is only $1.4 billion.

Rovio or another game developer could make exclusives to help Google+ regain momentum.

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Interest in Google+ seems to be fadingfast, and the introduction of a handful of games didn't do much to rekindle it. But what if Google bought a game developer who could create fantastic exclusives for the platform? It's probably too late for Zynga, but other big names like Angry Birds creator Rovio (which is seeking to raise a round at a $1.2 billion valuation) or Big Fish might fit the bill.

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Google bought travel information service ITA for $700 million earlier this year to make its travel results better, so why not take the next step and buy this travel-deals service? More than 24 million customers sign up for Travelzoo's weekly emails, which contain deals from more than 2,000 advertisers.

The company isn't cheap -- it's valued at more than $500 million despite having about $130 million in sales and a net loss of about $2 million over the last four quarters.

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Google has never been interested in being a Web portal or big editorial site -- the margins aren't good enough, and Google is an engineering company. (Although imagine how Kara Swisher's head would explode if TechCrunch was suddenly part of Google.)

But private equity firms are rumored to be circling AOL, and if they carved it up into pieces, the ad network would be a great fit for Google. AOL's display ad network is the third-largest in the U.S., behind Google and Yahoo, and with the entire company valued at only $1.6 billion, the ad business would be easily affordable.

The only problem: antitrust regulators are already taking a hard look at Google's advertising dominance, so they might block the deal.

Rovi has lots of hooks into video in the living room, which would be great for Google TV.

Rovi

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Formerly Macrovision, Rovi is a behind-the-scenes provider of technology used in digital video, such as the on-screen program guides used by cable and satellite TV providers, an on-demand movie streaming system used to power online stores from companies like Best Buy and Sears, and core video technology (DivX) that consumer electronics companies like Sony pack into their products.

Not to mention a burgeoning advertising platform that provides ads within the on-screen TV guides to more than 30 million households.

Rovi's market cap is just over $5 billion. Buying it would signal that Google is serious about the living room -- just like buying Motorola showed how serious it was about mobile.

But after a strong launch, interest seems to be waning -- a lot of people signed up, but various statistics suggest most of them aren't spending a lot of time there. If Google+ doesn't get some serious uptake by the end of the year, Google may have no choice but to pay up to get Twitter's built-in audience of millions.

Plus -- Apple just integrated Twitter into iOS 5. Imagine how sweet it would feel for Google to snatch that win away and integrate Twitter into Android as well.

NVIDIA would help Google design its own mobile processors -- just like Apple does for the iPhone.

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Motorola builds phones, but it relies on third parties like Qualcomm and NVIDIA to create the actual chips that go into those phones (based on ARM technology). But Apple designs its own ARM processors. If Google really wants to match Apple, buying NVIDIA -- whose market cap is around $8 billion -- would be a quick way in.

Sprint would be the second part of a huge one-two punch.

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Motorola gave Google the hardware. Buying Sprint would give Google an unstoppable distribution channel, plus full control over the Android experience -- hardware, software, and wireless service. Plus, Sprint owns a lot of valuable spectrum. It's valued at more than $11 billion, meaning Google would probably have to pay upwards of $15 billion to secure the deal.

But what if that was strategic misdirection? Enterprise software is a huge business, with tens of billions in annual sales -- think Microsoft, Oracle, SAP, IBM, and HP, just to start -- but after more than five years in the business, Google still books less than $1 billion a year from Gmail and Apps.

The software-as-a-service revolution is ten years old, and Salesforce is the undisputed leader -- more than 45,000 people showed up for its Dreamforce conference last week. It's highly valued, with a market cap of more than $16 billion versus very low earnings, but it's on track for $2 billion in sales this year and has tons of high-profile customers.

If Salesforce seems too big and rich, Google could roll up a bunch of smaller enterprise startups like Jive (where Chrome VP Sundar Pichai is on the board) and Box.net.